The high and the low do NOT share the same ground so I believe you can rule out a ground problem. So we will go after the hot side. Your headlight switch position makes a difference as far as what all comes into play. In On mode your BCM is bypassed and the switch directly feeds power to the headlamp relay coil effectively bypassing the day/night sensor circuit in tandem with the BCM. In auto mode your BCM comes into play and energizes the headlamp relay when the BCM is in night mode via the Day/Night sensor (thats the little smoked globe lens on top of the dash near the windshield).
There is more than one fuse that will kill your headlights. Double check Fuse marked TBC 10a (under hood). This is the fuse that feeds both of the above modes (Auto and On) and does nothing more than provide power to the headlamp relay coil. Without this fuse being good or associated wiring you are without headlights. If that all checks out then.....
I would suspect the headlamp relay itself. [during this check your headlight switch must be in on mode instead of auto] Check for power at the fuses marked LT HDLP and RT HDLP.(both sides of the fuse) Your headlamps are fed power actually by these two fuses (one for left side and one for the right side) but these fuses will be dead if the headlamp relay has a bad coil, no power to its coil, burnt internal contact (these contacts feed LT and RT HDLP fuses). It is unlikely that both the left and right side headlamp fuses blew at the same time unless you have a major wiring problem.
I suspect the above will find your problem. If it doesnt then post all results you find for the above. You could have a bad headlight switch, bad wiring, etc. If you are lucky you just need a new headlamp relay. Any auto parts store will have it if thats the culprit.